Welcome to the Quanta Audio Edition.

In each of these bi-weekly episodes, we bring you a story direct from the Quanta website

about developments in basic science and mathematics.

I'm Susan Vallett.

Individual molecules create the complex motion of fluids. Three mathematicians now

have proven that mathematically. It not only advances a key mathematical problem, but

it also illuminates why time can't flow in reverse. That's next.

Quantum Magazine is an editorially independent online publication supported by the Simon's Foundation to enhance public understanding of science.

At the turn of the 20th century, the renowned mathematician David Hilbert had a grand ambition

to bring a more rigorous mathematical way of thinking into the world of physics.

At the time, physicists were still plagued by debates about basic definitions. What is heat?

How are molecules structured? Hilbert hoped that the formal logic of mathematics could provide

guidance. On the morning of August 8 8, 1900, he delivered a list of

23 key math problems to the International Congress of Mathematicians. Number six was a big one.

Produce airtight proofs of the laws of physics. The scope of Hilbert's sixth problem was enormous. He asked to treat in the

same manner as geometry by means of axioms, those physical sciences in which mathematics plays an

important part. Dave Levermore, a mathematician at the University of Maryland, says Hilbert's challenge to axiomatize

physics was really a program. Levermore says the way the sixth problem is actually stated,

it's never going to be solved. But Hilbert provided a starting point. To study different

properties of a gas, say the speed of its molecules or its

average temperature, physicists use different equations. In particular, they use one set of

equations to describe how individual molecules in a gas move, and another to describe the behavior

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